TSTP Solution File: SET121-7 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET121-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:56:02 EDT 2023
% Result : Unsatisfiable 204.64s 179.54s
% Output : CNFRefutation 204.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 82
% Syntax : Number of formulae : 194 ( 73 unt; 51 typ; 0 def)
% Number of atoms : 235 ( 120 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 174 ( 82 ~; 92 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 67 ( 41 >; 26 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 42 ( 42 usr; 10 con; 0-3 aty)
% Number of variables : 146 (; 146 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ homomorphism > compatible > subclass > member > single_valued_class > operation > one_to_one > inductive > function > restrict > range > not_homomorphism2 > not_homomorphism1 > domain > unordered_pair > union > symmetric_difference > ordered_pair > not_subclass_element > intersection > image > cross_product > compose > apply > #nlpp > sum_class > successor > singleton > second > rotate > regular > range_of > power_class > member_of1 > member_of > inverse > flip > first > domain_of > diagonalise > complement > cantor > y > x > universal_class > successor_relation > subset_relation > omega > null_class > identity_relation > element_relation > choice
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(omega,type,
omega: $i ).
tff(null_class,type,
null_class: $i ).
tff(rotate,type,
rotate: $i > $i ).
tff(subclass,type,
subclass: ( $i * $i ) > $o ).
tff(singleton,type,
singleton: $i > $i ).
tff(single_valued_class,type,
single_valued_class: $i > $o ).
tff(operation,type,
operation: $i > $o ).
tff(sum_class,type,
sum_class: $i > $i ).
tff(x,type,
x: $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(compatible,type,
compatible: ( $i * $i * $i ) > $o ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(regular,type,
regular: $i > $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff(element_relation,type,
element_relation: $i ).
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff(second,type,
second: $i > $i ).
tff(union,type,
union: ( $i * $i ) > $i ).
tff(function,type,
function: $i > $o ).
tff(symmetric_difference,type,
symmetric_difference: ( $i * $i ) > $i ).
tff(flip,type,
flip: $i > $i ).
tff(power_class,type,
power_class: $i > $i ).
tff(cross_product,type,
cross_product: ( $i * $i ) > $i ).
tff(choice,type,
choice: $i ).
tff(y,type,
y: $i ).
tff(subset_relation,type,
subset_relation: $i ).
tff(restrict,type,
restrict: ( $i * $i * $i ) > $i ).
tff(complement,type,
complement: $i > $i ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff(member_of1,type,
member_of1: $i > $i ).
tff(not_subclass_element,type,
not_subclass_element: ( $i * $i ) > $i ).
tff(member_of,type,
member_of: $i > $i ).
tff(range,type,
range: ( $i * $i * $i ) > $i ).
tff(first,type,
first: $i > $i ).
tff(diagonalise,type,
diagonalise: $i > $i ).
tff(homomorphism,type,
homomorphism: ( $i * $i * $i ) > $o ).
tff(cantor,type,
cantor: $i > $i ).
tff(image,type,
image: ( $i * $i ) > $i ).
tff(range_of,type,
range_of: $i > $i ).
tff(inductive,type,
inductive: $i > $o ).
tff(domain,type,
domain: ( $i * $i * $i ) > $i ).
tff(compose,type,
compose: ( $i * $i ) > $i ).
tff(domain_of,type,
domain_of: $i > $i ).
tff(not_homomorphism2,type,
not_homomorphism2: ( $i * $i * $i ) > $i ).
tff(successor,type,
successor: $i > $i ).
tff(successor_relation,type,
successor_relation: $i ).
tff(identity_relation,type,
identity_relation: $i ).
tff(not_homomorphism1,type,
not_homomorphism1: ( $i * $i * $i ) > $i ).
tff(universal_class,type,
universal_class: $i ).
tff(f_369,axiom,
inductive(omega),
file(unknown,unknown) ).
tff(f_1074,axiom,
! [X] :
( ( ordered_pair(first(X),second(X)) = X )
| ( first(X) = X ) ),
file(unknown,unknown) ).
tff(f_1066,axiom,
! [X] :
( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| ( first(X) = X ) ),
file(unknown,unknown) ).
tff(f_1102,axiom,
~ member(y,universal_class),
file(unknown,unknown) ).
tff(f_848,axiom,
! [X] :
( member(X,universal_class)
| ( singleton(X) = null_class ) ),
file(unknown,unknown) ).
tff(f_129,axiom,
! [X,Y] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ),
file(unknown,unknown) ).
tff(f_985,axiom,
! [X,Y] :
( ( unordered_pair(singleton(X),unordered_pair(X,null_class)) = ordered_pair(X,Y) )
| member(Y,universal_class) ),
file(unknown,unknown) ).
tff(f_151,axiom,
! [U,X,V,Y] :
( ~ member(U,X)
| ~ member(V,Y)
| member(ordered_pair(U,V),cross_product(X,Y)) ),
file(unknown,unknown) ).
tff(f_758,axiom,
! [X,Y] :
( member(X,universal_class)
| ( unordered_pair(X,Y) = singleton(Y) ) ),
file(unknown,unknown) ).
tff(f_490,axiom,
! [Y] :
( ~ member(Y,universal_class)
| ( Y = null_class )
| member(apply(choice,Y),Y) ),
file(unknown,unknown) ).
tff(f_835,axiom,
! [X] :
( ~ member(X,universal_class)
| ( singleton(X) != null_class ) ),
file(unknown,unknown) ).
tff(f_754,axiom,
! [Y,X] :
( member(Y,universal_class)
| ( unordered_pair(X,Y) = singleton(X) ) ),
file(unknown,unknown) ).
tff(f_744,axiom,
! [X,Y] : ( unordered_pair(X,Y) = unordered_pair(Y,X) ),
file(unknown,unknown) ).
tff(f_661,axiom,
! [U,V,X,Y] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) ),
file(unknown,unknown) ).
tff(f_666,axiom,
! [U,V,X,Y] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) ),
file(unknown,unknown) ).
tff(f_1104,axiom,
first(ordered_pair(x,y)) != ordered_pair(x,y),
file(unknown,unknown) ).
tff(f_980,axiom,
! [X,Y] : member(unordered_pair(X,singleton(Y)),ordered_pair(X,Y)),
file(unknown,unknown) ).
tff(f_898,axiom,
! [X] :
( ( singleton(member_of(X)) = X )
| ( member_of(X) = X ) ),
file(unknown,unknown) ).
tff(f_375,axiom,
member(omega,universal_class),
file(unknown,unknown) ).
tff(f_931,axiom,
! [X,Y] :
( ( singleton(member_of(X)) != X )
| ~ member(Y,X)
| ( member_of(X) = Y ) ),
file(unknown,unknown) ).
tff(f_865,axiom,
! [X,Y] :
( ( singleton(X) != singleton(Y) )
| ~ member(Y,universal_class)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_905,axiom,
! [U] :
( ~ member(U,universal_class)
| ( member_of(singleton(U)) = U ) ),
file(unknown,unknown) ).
tff(f_471,axiom,
! [X] :
( ( X = null_class )
| member(regular(X),X) ),
file(unknown,unknown) ).
tff(f_724,axiom,
! [Z] : ~ member(Z,null_class),
file(unknown,unknown) ).
tff(f_475,axiom,
! [X] :
( ( X = null_class )
| ( intersection(X,regular(X)) = null_class ) ),
file(unknown,unknown) ).
tff(f_200,axiom,
! [Z,X,Y] :
( ~ member(Z,X)
| ~ member(Z,Y)
| member(Z,intersection(X,Y)) ),
file(unknown,unknown) ).
tff(f_818,axiom,
! [X] : member(singleton(X),universal_class),
file(unknown,unknown) ).
tff(f_350,axiom,
! [X] :
( ~ inductive(X)
| member(null_class,X) ),
file(unknown,unknown) ).
tff(f_374,axiom,
! [Y] :
( ~ inductive(Y)
| subclass(omega,Y) ),
file(unknown,unknown) ).
tff(f_945,axiom,
! [X,Y] :
( ~ subclass(X,singleton(Y))
| ( X = null_class )
| ( singleton(Y) = X ) ),
file(unknown,unknown) ).
tff(f_843,axiom,
! [Y,X] :
( ~ member(Y,singleton(X))
| ( Y = X ) ),
file(unknown,unknown) ).
tff(c_100,plain,
inductive(omega),
inference(cnfTransformation,[status(thm)],[f_369]) ).
tff(c_324,plain,
! [X_306] :
( ( first(X_306) = X_306 )
| ( ordered_pair(first(X_306),second(X_306)) = X_306 ) ),
inference(cnfTransformation,[status(thm)],[f_1074]) ).
tff(c_687100,plain,
! [X_542985] :
( ( first(X_542985) = X_542985 )
| member(ordered_pair(first(X_542985),second(X_542985)),cross_product(universal_class,universal_class)) ),
inference(cnfTransformation,[status(thm)],[f_1066]) ).
tff(c_751557,plain,
! [X_543827] :
( ( first(X_543827) = X_543827 )
| member(X_543827,cross_product(universal_class,universal_class))
| ( first(X_543827) = X_543827 ) ),
inference(superposition,[status(thm),theory(equality)],[c_324,c_687100]) ).
tff(c_336,plain,
~ member(y,universal_class),
inference(cnfTransformation,[status(thm)],[f_1102]) ).
tff(c_403,plain,
! [X_331] :
( ( singleton(X_331) = null_class )
| member(X_331,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_848]) ).
tff(c_407,plain,
singleton(y) = null_class,
inference(resolution,[status(thm)],[c_403,c_336]) ).
tff(c_109600,plain,
! [X_1859,Y_1860] : ( unordered_pair(singleton(X_1859),unordered_pair(X_1859,singleton(Y_1860))) = ordered_pair(X_1859,Y_1860) ),
inference(cnfTransformation,[status(thm)],[f_129]) ).
tff(c_109732,plain,
! [X_1859] : ( unordered_pair(singleton(X_1859),unordered_pair(X_1859,null_class)) = ordered_pair(X_1859,y) ),
inference(superposition,[status(thm),theory(equality)],[c_407,c_109600]) ).
tff(c_296,plain,
! [Y_281,X_280] :
( member(Y_281,universal_class)
| ( unordered_pair(singleton(X_280),unordered_pair(X_280,null_class)) = ordered_pair(X_280,Y_281) ) ),
inference(cnfTransformation,[status(thm)],[f_985]) ).
tff(c_712343,plain,
! [Y_543445,X_543446] :
( member(Y_543445,universal_class)
| ( ordered_pair(X_543446,y) = ordered_pair(X_543446,Y_543445) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_109732,c_296]) ).
tff(c_32,plain,
! [U_35,V_37,X_36,Y_38] :
( member(ordered_pair(U_35,V_37),cross_product(X_36,Y_38))
| ~ member(V_37,Y_38)
| ~ member(U_35,X_36) ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_1071,plain,
! [X_404,Y_405] :
( ( unordered_pair(X_404,Y_405) = singleton(Y_405) )
| member(X_404,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_758]) ).
tff(c_1134,plain,
! [Y_405] : ( unordered_pair(y,Y_405) = singleton(Y_405) ),
inference(resolution,[status(thm)],[c_1071,c_336]) ).
tff(c_109729,plain,
! [Y_1860] : ( unordered_pair(null_class,unordered_pair(y,singleton(Y_1860))) = ordered_pair(y,Y_1860) ),
inference(superposition,[status(thm),theory(equality)],[c_407,c_109600]) ).
tff(c_109760,plain,
! [Y_1860] : ( unordered_pair(null_class,singleton(singleton(Y_1860))) = ordered_pair(y,Y_1860) ),
inference(demodulation,[status(thm),theory(equality)],[c_1134,c_109729]) ).
tff(c_252,plain,
! [X_247] :
( ( singleton(X_247) = null_class )
| member(X_247,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_848]) ).
tff(c_4783,plain,
! [Y_572] :
( member(apply(choice,Y_572),Y_572)
| ( null_class = Y_572 )
| ~ member(Y_572,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_490]) ).
tff(c_246,plain,
! [X_244] :
( ( singleton(X_244) != null_class )
| ~ member(X_244,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_835]) ).
tff(c_4833,plain,
( ( singleton(apply(choice,universal_class)) != null_class )
| ( universal_class = null_class )
| ~ member(universal_class,universal_class) ),
inference(resolution,[status(thm)],[c_4783,c_246]) ).
tff(c_701521,plain,
~ member(universal_class,universal_class),
inference(splitLeft,[status(thm)],[c_4833]) ).
tff(c_701588,plain,
singleton(universal_class) = null_class,
inference(resolution,[status(thm)],[c_252,c_701521]) ).
tff(c_222,plain,
! [X_218,Y_217] :
( ( unordered_pair(X_218,Y_217) = singleton(X_218) )
| member(Y_217,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_754]) ).
tff(c_702505,plain,
! [X_543314] : ( unordered_pair(X_543314,universal_class) = singleton(X_543314) ),
inference(resolution,[status(thm)],[c_222,c_701521]) ).
tff(c_216,plain,
! [Y_212,X_211] : ( unordered_pair(Y_212,X_211) = unordered_pair(X_211,Y_212) ),
inference(cnfTransformation,[status(thm)],[f_744]) ).
tff(c_109726,plain,
! [Y_212,Y_1860] : ( unordered_pair(singleton(Y_212),unordered_pair(singleton(Y_1860),Y_212)) = ordered_pair(Y_212,Y_1860) ),
inference(superposition,[status(thm),theory(equality)],[c_216,c_109600]) ).
tff(c_702547,plain,
! [Y_1860] : ( unordered_pair(singleton(universal_class),singleton(singleton(Y_1860))) = ordered_pair(universal_class,Y_1860) ),
inference(superposition,[status(thm),theory(equality)],[c_702505,c_109726]) ).
tff(c_702852,plain,
! [Y_543317] : ( ordered_pair(y,Y_543317) = ordered_pair(universal_class,Y_543317) ),
inference(demodulation,[status(thm),theory(equality)],[c_109760,c_701588,c_702547]) ).
tff(c_188,plain,
! [U_185,V_186,X_187,Y_188] :
( member(U_185,universal_class)
| ~ member(ordered_pair(U_185,V_186),cross_product(X_187,Y_188)) ),
inference(cnfTransformation,[status(thm)],[f_661]) ).
tff(c_702965,plain,
! [Y_543317,X_187,Y_188] :
( member(y,universal_class)
| ~ member(ordered_pair(universal_class,Y_543317),cross_product(X_187,Y_188)) ),
inference(superposition,[status(thm),theory(equality)],[c_702852,c_188]) ).
tff(c_704691,plain,
! [Y_543339,X_543340,Y_543341] : ~ member(ordered_pair(universal_class,Y_543339),cross_product(X_543340,Y_543341)),
inference(negUnitSimplification,[status(thm)],[c_336,c_702965]) ).
tff(c_704708,plain,
! [V_37,Y_38,X_36] :
( ~ member(V_37,Y_38)
| ~ member(universal_class,X_36) ),
inference(resolution,[status(thm)],[c_32,c_704691]) ).
tff(c_704711,plain,
! [X_36] : ~ member(universal_class,X_36),
inference(splitLeft,[status(thm)],[c_704708]) ).
tff(c_713047,plain,
! [X_543447] : ( ordered_pair(X_543447,y) = ordered_pair(X_543447,universal_class) ),
inference(resolution,[status(thm)],[c_712343,c_704711]) ).
tff(c_190,plain,
! [V_190,U_189,X_191,Y_192] :
( member(V_190,universal_class)
| ~ member(ordered_pair(U_189,V_190),cross_product(X_191,Y_192)) ),
inference(cnfTransformation,[status(thm)],[f_666]) ).
tff(c_713286,plain,
! [X_543447,X_191,Y_192] :
( member(y,universal_class)
| ~ member(ordered_pair(X_543447,universal_class),cross_product(X_191,Y_192)) ),
inference(superposition,[status(thm),theory(equality)],[c_713047,c_190]) ).
tff(c_713359,plain,
! [X_543447,X_191,Y_192] : ~ member(ordered_pair(X_543447,universal_class),cross_product(X_191,Y_192)),
inference(negUnitSimplification,[status(thm)],[c_336,c_713286]) ).
tff(c_751687,plain,
! [X_543447] : ( first(ordered_pair(X_543447,universal_class)) = ordered_pair(X_543447,universal_class) ),
inference(resolution,[status(thm)],[c_751557,c_713359]) ).
tff(c_712946,plain,
! [X_543446] : ( ordered_pair(X_543446,y) = ordered_pair(X_543446,universal_class) ),
inference(resolution,[status(thm)],[c_712343,c_704711]) ).
tff(c_338,plain,
first(ordered_pair(x,y)) != ordered_pair(x,y),
inference(cnfTransformation,[status(thm)],[f_1104]) ).
tff(c_713041,plain,
first(ordered_pair(x,universal_class)) != ordered_pair(x,universal_class),
inference(demodulation,[status(thm),theory(equality)],[c_712946,c_712946,c_338]) ).
tff(c_752308,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_751687,c_713041]) ).
tff(c_752309,plain,
! [V_37,Y_38] : ~ member(V_37,Y_38),
inference(splitRight,[status(thm)],[c_704708]) ).
tff(c_702725,plain,
! [Y_1860] : ( ordered_pair(y,Y_1860) = ordered_pair(universal_class,Y_1860) ),
inference(demodulation,[status(thm),theory(equality)],[c_109760,c_701588,c_702547]) ).
tff(c_110062,plain,
! [Y_1878] : ( unordered_pair(null_class,singleton(singleton(Y_1878))) = ordered_pair(y,Y_1878) ),
inference(demodulation,[status(thm),theory(equality)],[c_1134,c_109729]) ).
tff(c_110147,plain,
unordered_pair(null_class,singleton(null_class)) = ordered_pair(y,y),
inference(superposition,[status(thm),theory(equality)],[c_407,c_110062]) ).
tff(c_702844,plain,
unordered_pair(null_class,singleton(null_class)) = ordered_pair(universal_class,y),
inference(demodulation,[status(thm),theory(equality)],[c_702725,c_110147]) ).
tff(c_701829,plain,
unordered_pair(null_class,singleton(null_class)) = ordered_pair(y,universal_class),
inference(superposition,[status(thm),theory(equality)],[c_701588,c_109760]) ).
tff(c_703990,plain,
ordered_pair(universal_class,y) = ordered_pair(universal_class,universal_class),
inference(demodulation,[status(thm),theory(equality)],[c_702844,c_702725,c_701829]) ).
tff(c_703992,plain,
unordered_pair(null_class,singleton(null_class)) = ordered_pair(universal_class,universal_class),
inference(demodulation,[status(thm),theory(equality)],[c_703990,c_702844]) ).
tff(c_294,plain,
! [X_278,Y_279] : member(unordered_pair(X_278,singleton(Y_279)),ordered_pair(X_278,Y_279)),
inference(cnfTransformation,[status(thm)],[f_980]) ).
tff(c_704442,plain,
member(ordered_pair(universal_class,universal_class),ordered_pair(null_class,null_class)),
inference(superposition,[status(thm),theory(equality)],[c_703992,c_294]) ).
tff(c_752469,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_752309,c_704442]) ).
tff(c_752471,plain,
member(universal_class,universal_class),
inference(splitRight,[status(thm)],[c_4833]) ).
tff(c_752511,plain,
singleton(universal_class) != null_class,
inference(resolution,[status(thm)],[c_752471,c_246]) ).
tff(c_266,plain,
! [X_258] :
( ( member_of(X_258) = X_258 )
| ( singleton(member_of(X_258)) = X_258 ) ),
inference(cnfTransformation,[status(thm)],[f_898]) ).
tff(c_104,plain,
member(omega,universal_class),
inference(cnfTransformation,[status(thm)],[f_375]) ).
tff(c_4169,plain,
! [X_549,Y_550] :
( ( member_of(X_549) = Y_550 )
| ~ member(Y_550,X_549)
| ( singleton(member_of(X_549)) != X_549 ) ),
inference(cnfTransformation,[status(thm)],[f_931]) ).
tff(c_4309,plain,
( ( member_of(universal_class) = omega )
| ( singleton(member_of(universal_class)) != universal_class ) ),
inference(resolution,[status(thm)],[c_104,c_4169]) ).
tff(c_4311,plain,
singleton(member_of(universal_class)) != universal_class,
inference(splitLeft,[status(thm)],[c_4309]) ).
tff(c_4315,plain,
member_of(universal_class) = universal_class,
inference(superposition,[status(thm),theory(equality)],[c_266,c_4311]) ).
tff(c_4316,plain,
singleton(universal_class) != universal_class,
inference(demodulation,[status(thm),theory(equality)],[c_4315,c_4311]) ).
tff(c_256,plain,
! [Y_251,X_250] :
( ( Y_251 = X_250 )
| ~ member(Y_251,universal_class)
| ( singleton(Y_251) != singleton(X_250) ) ),
inference(cnfTransformation,[status(thm)],[f_865]) ).
tff(c_752517,plain,
! [X_543833] :
( ( universal_class = X_543833 )
| ( singleton(universal_class) != singleton(X_543833) ) ),
inference(resolution,[status(thm)],[c_752471,c_256]) ).
tff(c_752532,plain,
! [X_258] :
( ( member_of(X_258) = universal_class )
| ( singleton(universal_class) != X_258 )
| ( member_of(X_258) = X_258 ) ),
inference(superposition,[status(thm),theory(equality)],[c_266,c_752517]) ).
tff(c_781901,plain,
( ( member_of(singleton(universal_class)) = universal_class )
| ( member_of(singleton(universal_class)) = singleton(universal_class) ) ),
inference(reflexivity,[status(thm),theory(equality)],[c_752532]) ).
tff(c_784555,plain,
member_of(singleton(universal_class)) = singleton(universal_class),
inference(splitLeft,[status(thm)],[c_781901]) ).
tff(c_268,plain,
! [U_259] :
( ( member_of(singleton(U_259)) = U_259 )
| ~ member(U_259,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_905]) ).
tff(c_784674,plain,
( ( singleton(universal_class) = universal_class )
| ~ member(universal_class,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_784555,c_268]) ).
tff(c_784728,plain,
singleton(universal_class) = universal_class,
inference(demodulation,[status(thm),theory(equality)],[c_752471,c_784674]) ).
tff(c_784730,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4316,c_784728]) ).
tff(c_784731,plain,
member_of(singleton(universal_class)) = universal_class,
inference(splitRight,[status(thm)],[c_781901]) ).
tff(c_132,plain,
! [X_131] :
( member(regular(X_131),X_131)
| ( null_class = X_131 ) ),
inference(cnfTransformation,[status(thm)],[f_471]) ).
tff(c_4302,plain,
! [X_131] :
( ( regular(X_131) = member_of(X_131) )
| ( singleton(member_of(X_131)) != X_131 )
| ( null_class = X_131 ) ),
inference(resolution,[status(thm)],[c_132,c_4169]) ).
tff(c_784781,plain,
( ( regular(singleton(universal_class)) = member_of(singleton(universal_class)) )
| ( singleton(universal_class) = null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_784731,c_4302]) ).
tff(c_784869,plain,
( ( regular(singleton(universal_class)) = universal_class )
| ( singleton(universal_class) = null_class ) ),
inference(demodulation,[status(thm),theory(equality)],[c_784731,c_784781]) ).
tff(c_784870,plain,
regular(singleton(universal_class)) = universal_class,
inference(negUnitSimplification,[status(thm)],[c_752511,c_784869]) ).
tff(c_784948,plain,
( member(universal_class,singleton(universal_class))
| ( singleton(universal_class) = null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_784870,c_132]) ).
tff(c_784979,plain,
member(universal_class,singleton(universal_class)),
inference(negUnitSimplification,[status(thm)],[c_752511,c_784948]) ).
tff(c_206,plain,
! [Z_207] : ~ member(Z_207,null_class),
inference(cnfTransformation,[status(thm)],[f_724]) ).
tff(c_134,plain,
! [X_132] :
( ( intersection(X_132,regular(X_132)) = null_class )
| ( null_class = X_132 ) ),
inference(cnfTransformation,[status(thm)],[f_475]) ).
tff(c_110550,plain,
! [Z_1894,X_1895,Y_1896] :
( member(Z_1894,intersection(X_1895,Y_1896))
| ~ member(Z_1894,Y_1896)
| ~ member(Z_1894,X_1895) ),
inference(cnfTransformation,[status(thm)],[f_200]) ).
tff(c_110589,plain,
! [Z_1894,X_132] :
( member(Z_1894,null_class)
| ~ member(Z_1894,regular(X_132))
| ~ member(Z_1894,X_132)
| ( null_class = X_132 ) ),
inference(superposition,[status(thm),theory(equality)],[c_134,c_110550]) ).
tff(c_110605,plain,
! [Z_1894,X_132] :
( ~ member(Z_1894,regular(X_132))
| ~ member(Z_1894,X_132)
| ( null_class = X_132 ) ),
inference(negUnitSimplification,[status(thm)],[c_206,c_110589]) ).
tff(c_784933,plain,
! [Z_1894] :
( ~ member(Z_1894,universal_class)
| ~ member(Z_1894,singleton(universal_class))
| ( singleton(universal_class) = null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_784870,c_110605]) ).
tff(c_785773,plain,
! [Z_544191] :
( ~ member(Z_544191,universal_class)
| ~ member(Z_544191,singleton(universal_class)) ),
inference(negUnitSimplification,[status(thm)],[c_752511,c_784933]) ).
tff(c_785776,plain,
~ member(universal_class,universal_class),
inference(resolution,[status(thm)],[c_784979,c_785773]) ).
tff(c_785910,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_752471,c_785776]) ).
tff(c_785911,plain,
member_of(universal_class) = omega,
inference(splitRight,[status(thm)],[c_4309]) ).
tff(c_785912,plain,
singleton(member_of(universal_class)) = universal_class,
inference(splitRight,[status(thm)],[c_4309]) ).
tff(c_785962,plain,
singleton(omega) = universal_class,
inference(demodulation,[status(thm),theory(equality)],[c_785911,c_785912]) ).
tff(c_240,plain,
! [X_240] : member(singleton(X_240),universal_class),
inference(cnfTransformation,[status(thm)],[f_818]) ).
tff(c_786117,plain,
member(universal_class,universal_class),
inference(superposition,[status(thm),theory(equality)],[c_785962,c_240]) ).
tff(c_276,plain,
! [X_263,Y_264] :
( ( member_of(X_263) = Y_264 )
| ~ member(Y_264,X_263)
| ( singleton(member_of(X_263)) != X_263 ) ),
inference(cnfTransformation,[status(thm)],[f_931]) ).
tff(c_786167,plain,
( ( member_of(universal_class) = universal_class )
| ( singleton(member_of(universal_class)) != universal_class ) ),
inference(resolution,[status(thm)],[c_786117,c_276]) ).
tff(c_786177,plain,
universal_class = omega,
inference(demodulation,[status(thm),theory(equality)],[c_785962,c_785911,c_785911,c_786167]) ).
tff(c_385,plain,
! [X_326] :
( member(null_class,X_326)
| ~ inductive(X_326) ),
inference(cnfTransformation,[status(thm)],[f_350]) ).
tff(c_390,plain,
~ inductive(null_class),
inference(resolution,[status(thm)],[c_385,c_206]) ).
tff(c_102,plain,
! [Y_109] :
( subclass(omega,Y_109)
| ~ inductive(Y_109) ),
inference(cnfTransformation,[status(thm)],[f_374]) ).
tff(c_2540,plain,
! [Y_484,X_485] :
( ( singleton(Y_484) = X_485 )
| ( null_class = X_485 )
| ~ subclass(X_485,singleton(Y_484)) ),
inference(cnfTransformation,[status(thm)],[f_945]) ).
tff(c_2573,plain,
! [Y_484] :
( ( singleton(Y_484) = omega )
| ( omega = null_class )
| ~ inductive(singleton(Y_484)) ),
inference(resolution,[status(thm)],[c_102,c_2540]) ).
tff(c_2758,plain,
omega = null_class,
inference(splitLeft,[status(thm)],[c_2573]) ).
tff(c_2763,plain,
inductive(null_class),
inference(demodulation,[status(thm),theory(equality)],[c_2758,c_100]) ).
tff(c_2767,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_390,c_2763]) ).
tff(c_2769,plain,
omega != null_class,
inference(splitRight,[status(thm)],[c_2573]) ).
tff(c_94,plain,
! [X_106] :
( member(null_class,X_106)
| ~ inductive(X_106) ),
inference(cnfTransformation,[status(thm)],[f_350]) ).
tff(c_518,plain,
! [Y_347,X_348] :
( ( Y_347 = X_348 )
| ~ member(Y_347,singleton(X_348)) ),
inference(cnfTransformation,[status(thm)],[f_843]) ).
tff(c_534,plain,
! [X_348] :
( ( null_class = X_348 )
| ~ inductive(singleton(X_348)) ),
inference(resolution,[status(thm)],[c_94,c_518]) ).
tff(c_786103,plain,
( ( omega = null_class )
| ~ inductive(universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_785962,c_534]) ).
tff(c_786157,plain,
~ inductive(universal_class),
inference(negUnitSimplification,[status(thm)],[c_2769,c_786103]) ).
tff(c_786185,plain,
~ inductive(omega),
inference(demodulation,[status(thm),theory(equality)],[c_786177,c_786157]) ).
tff(c_786250,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_100,c_786185]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET121-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.11/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 16:52:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 204.64/179.54 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 204.77/179.56
% 204.77/179.56 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 204.77/179.60
% 204.77/179.60 Inference rules
% 204.77/179.60 ----------------------
% 204.77/179.60 #Ref : 286
% 204.77/179.60 #Sup : 212063
% 204.77/179.60 #Fact : 66
% 204.77/179.60 #Define : 0
% 204.77/179.60 #Split : 740
% 204.77/179.60 #Chain : 0
% 204.77/179.60 #Close : 0
% 204.77/179.60
% 204.77/179.60 Ordering : KBO
% 204.77/179.60
% 204.77/179.60 Simplification rules
% 204.77/179.60 ----------------------
% 204.77/179.60 #Subsume : 53176
% 204.77/179.60 #Demod : 93403
% 204.77/179.60 #Tautology : 44290
% 204.77/179.60 #SimpNegUnit : 14899
% 204.77/179.60 #BackRed : 4144
% 204.77/179.60
% 204.77/179.60 #Partial instantiations: 74871
% 204.77/179.60 #Strategies tried : 1
% 204.77/179.60
% 204.77/179.60 Timing (in seconds)
% 204.77/179.60 ----------------------
% 204.77/179.61 Preprocessing : 0.84
% 204.77/179.61 Parsing : 0.39
% 204.77/179.61 CNF conversion : 0.06
% 204.77/179.61 Main loop : 177.72
% 204.77/179.61 Inferencing : 21.80
% 204.77/179.61 Reduction : 82.64
% 204.77/179.61 Demodulation : 60.99
% 204.77/179.61 BG Simplification : 0.91
% 204.77/179.61 Subsumption : 52.89
% 204.77/179.61 Abstraction : 1.62
% 204.77/179.61 MUC search : 0.00
% 204.77/179.61 Cooper : 0.00
% 204.77/179.61 Total : 178.65
% 204.77/179.61 Index Insertion : 0.00
% 204.77/179.61 Index Deletion : 0.00
% 204.77/179.61 Index Matching : 0.00
% 204.77/179.61 BG Taut test : 0.00
%------------------------------------------------------------------------------